{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "5c565407",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.io"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "fd63ebc9",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.io\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "# Load the .mat file\n",
    "mat_data = scipy.io.loadmat('Allen_Cahn.mat')\n",
    "\n",
    "# Following is the code to plot the data u vs x and t. u is 256*100\n",
    "# matrix. Use first 75 columns for training and 25 for testing :)\n",
    "\n",
    "# Access the variables stored in the .mat file\n",
    "# The variable names in the .mat file become keys in the loaded dictionary\n",
    "x = mat_data['x']\n",
    "t = mat_data['t']\n",
    "u = mat_data['u']\n",
    "\n",
    "# # Use the loaded variables as needed\n",
    "# print(x.shape)\n",
    "# print(t.shape)\n",
    "# print(u.shape)\n",
    "\n",
    "# X, T = np.meshgrid(x, t)\n",
    "# # Define custom color levels\n",
    "# c_levels = np.linspace(np.min(u), np.max(u), 100)\n",
    "\n",
    "# # Plot the contour\n",
    "# plt.figure()\n",
    "# plt.figure(figsize=(15, 5))\n",
    "# plt.contourf(T, X, u, levels=c_levels, cmap='coolwarm')\n",
    "# plt.xlabel('t')\n",
    "# plt.ylabel('x')\n",
    "# plt.title('Allen-cahn-Equation')\n",
    "# plt.colorbar()  # Add a colorbar for the contour levels\n",
    "# plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "2eaf77a3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(20301, 2)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.io\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "# Load the .mat file\n",
    "mat_data = scipy.io.loadmat('X.mat')\n",
    "\n",
    "X = mat_data['X']\n",
    "\n",
    "mat_data1 = scipy.io.loadmat('y_pred.mat')\n",
    "\n",
    "u1 = mat_data1['y_pred']\n",
    "\n",
    "np.set_printoptions(threshold=np.inf)\n",
    "\n",
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "37f3dd78",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(201, 101)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u1 = u1.reshape(101, 201)\n",
    "u1_new = u1.T\n",
    "u1_new.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "5641c6d9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tani (20301, 1)\n"
     ]
    }
   ],
   "source": [
    "# Load the .mat file\n",
    "mat_data2 = scipy.io.loadmat('y_true.mat')\n",
    "\n",
    "u2 = mat_data2['y_true']\n",
    "print(\"tani\", u2.shape)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d83063ad",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "64cb0a33",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1080x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "{'__header__': b'MATLAB 5.0 MAT-file Platform: posix, Created on: Fri Jul 21 17:01:43 2023',\n",
       " '__version__': '1.0',\n",
       " '__globals__': [],\n",
       " 'X': array([[-1.  ,  0.  ],\n",
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       "        [ 0.93,  1.  ],\n",
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       "        [ 0.98,  1.  ],\n",
       "        [ 0.99,  1.  ],\n",
       "        [ 1.  ,  1.  ]])}"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.io\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "\n",
    "X, T = np.meshgrid(x, t)\n",
    "\n",
    "# # Define custom color levels\n",
    "c_levels = np.linspace(np.min(u1_new),  np.max(u1_new), 100)\n",
    "\n",
    "# Plot the contour\n",
    "plt.figure()\n",
    "plt.figure(figsize=(15, 5))\n",
    "plt.contourf(T, X, u1_new.T, levels=c_levels, cmap='coolwarm')\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('x')\n",
    "plt.title('Allen-cahn-Equation')\n",
    "plt.colorbar()  # Add a colorbar for the contour levels\n",
    "plt.show()\n",
    "mat_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "bdd66d0b",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.io\n",
    "# Define the coRNNCell\n",
    "class coRNNCell(nn.Module):\n",
    "    def __init__(self, n_inp, n_hid, dt, gamma, epsilon):\n",
    "        super(coRNNCell, self).__init__()\n",
    "        self.dt = dt\n",
    "        self.gamma = gamma\n",
    "        self.epsilon = epsilon\n",
    "        self.i2h = nn.Linear(n_inp + n_hid + n_hid, n_hid)\n",
    "\n",
    "    def forward(self, x, hy, hz):\n",
    "        hz = hz + self.dt * (torch.tanh(self.i2h(torch.cat((x, hz, hy), 1)))\n",
    "                             - self.gamma * hy - self.epsilon * hz)\n",
    "        hy = hy + self.dt * hz\n",
    "\n",
    "        return hy, hz\n",
    "\n",
    "# Define the coRNN model\n",
    "class coRNN(nn.Module):\n",
    "    def __init__(self, n_inp, n_hid, n_out, dt, gamma, epsilon):\n",
    "        super(coRNN, self).__init__()\n",
    "        self.n_hid = n_hid\n",
    "        self.cell = coRNNCell(n_inp, n_hid, dt, gamma, epsilon)\n",
    "        self.readout = nn.Linear(n_hid, n_out)\n",
    "\n",
    "    def forward(self, x):\n",
    "        hy = torch.zeros(x.size(1), self.n_hid)\n",
    "        hz = torch.zeros(x.size(1), self.n_hid)\n",
    "\n",
    "        for t in range(x.size(0)):\n",
    "            hy, hz = self.cell(x[t], hy, hz)\n",
    "        output = self.readout(hy)\n",
    "\n",
    "        return output\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "c1edbcb7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<torch._C.Generator at 0x7f7ef46bd790>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Set random seed for reproducibility\n",
    "torch.manual_seed(42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "9e870afb",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Toy problem data\n",
    "input_size = 201  # number of columns in a dataset\n",
    "hidden_size = 32  # number of neurons\n",
    "output_size = 201\n",
    "sequence_length = 80  # number of sequences/ number of rows\n",
    "batch_size = 1\n",
    "num_epochs = 20000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "ed181dc1",
   "metadata": {},
   "outputs": [],
   "source": [
    "u1 = u1_new"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "d05b74dc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "test data shape (201,)\n",
      "input data shape (201, 80)\n",
      "Target data shape (201, 80)\n"
     ]
    }
   ],
   "source": [
    "input_data = u1_new[:, 0:80]\n",
    "target_data = u1_new[:, 1:81]\n",
    "\n",
    "test_data = u1_new[:, 80]\n",
    "#test_target = u1[:, 81:101]\n",
    "\n",
    "print(\"test data shape\", test_data.shape)\n",
    "#print(\"test target shape\", test_target.shape)\n",
    "\n",
    "print(\"input data shape\",input_data.shape)\n",
    "print(\"Target data shape\",target_data.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "e2f8359c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "input tensor shape torch.Size([1, 80, 201])\n",
      "Target tensor shape torch.Size([1, 80, 201])\n"
     ]
    }
   ],
   "source": [
    "# Convert data to tensors\n",
    "input_tensor = torch.tensor(input_data.T).view(batch_size, sequence_length, input_size).float()\n",
    "target_tensor = torch.tensor(target_data.T).view(batch_size, sequence_length, output_size).float()\n",
    "\n",
    "print(\"input tensor shape\",input_tensor.shape)\n",
    "print(\"Target tensor shape\",target_tensor.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "14aed18b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Convert test data to tensors\n",
    "test_tensor = torch.tensor(test_data.T).view(batch_size, 1, input_size).float()\n",
    "#test_target_tensor = torch.tensor(test_target.T).view(batch_size, 20, output_size).float()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "c258c108",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 10/20000, Loss: 0.42198160\n",
      "Epoch: 20/20000, Loss: 0.40791842\n",
      "Epoch: 30/20000, Loss: 0.39426807\n",
      "Epoch: 40/20000, Loss: 0.38114074\n",
      "Epoch: 50/20000, Loss: 0.36854243\n",
      "Epoch: 60/20000, Loss: 0.35645503\n",
      "Epoch: 70/20000, Loss: 0.34485063\n",
      "Epoch: 80/20000, Loss: 0.33370048\n",
      "Epoch: 90/20000, Loss: 0.32297829\n",
      "Epoch: 100/20000, Loss: 0.31266090\n",
      "Epoch: 110/20000, Loss: 0.30272791\n",
      "Epoch: 120/20000, Loss: 0.29316103\n",
      "Epoch: 130/20000, Loss: 0.28394392\n",
      "Epoch: 140/20000, Loss: 0.27506155\n",
      "Epoch: 150/20000, Loss: 0.26650006\n",
      "Epoch: 160/20000, Loss: 0.25824642\n",
      "Epoch: 170/20000, Loss: 0.25028861\n",
      "Epoch: 180/20000, Loss: 0.24261504\n",
      "Epoch: 190/20000, Loss: 0.23521499\n",
      "Epoch: 200/20000, Loss: 0.22807810\n",
      "Epoch: 210/20000, Loss: 0.22119458\n",
      "Epoch: 220/20000, Loss: 0.21455507\n",
      "Epoch: 230/20000, Loss: 0.20815067\n",
      "Epoch: 240/20000, Loss: 0.20197287\n",
      "Epoch: 250/20000, Loss: 0.19601355\n",
      "Epoch: 260/20000, Loss: 0.19026491\n",
      "Epoch: 270/20000, Loss: 0.18471950\n",
      "Epoch: 280/20000, Loss: 0.17937018\n",
      "Epoch: 290/20000, Loss: 0.17421009\n",
      "Epoch: 300/20000, Loss: 0.16923267\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/data/localhome/tkapoor/.local/lib/python3.8/site-packages/torch/nn/modules/loss.py:520: UserWarning: Using a target size (torch.Size([1, 80, 201])) that is different to the input size (torch.Size([80, 201])). This will likely lead to incorrect results due to broadcasting. Please ensure they have the same size.\n",
      "  return F.mse_loss(input, target, reduction=self.reduction)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 310/20000, Loss: 0.16443159\n",
      "Epoch: 320/20000, Loss: 0.15980081\n",
      "Epoch: 330/20000, Loss: 0.15533449\n",
      "Epoch: 340/20000, Loss: 0.15102704\n",
      "Epoch: 350/20000, Loss: 0.14687307\n",
      "Epoch: 360/20000, Loss: 0.14286737\n",
      "Epoch: 370/20000, Loss: 0.13900495\n",
      "Epoch: 380/20000, Loss: 0.13528100\n",
      "Epoch: 390/20000, Loss: 0.13169084\n",
      "Epoch: 400/20000, Loss: 0.12823002\n",
      "Epoch: 410/20000, Loss: 0.12489422\n",
      "Epoch: 420/20000, Loss: 0.12167923\n",
      "Epoch: 430/20000, Loss: 0.11858106\n",
      "Epoch: 440/20000, Loss: 0.11559581\n",
      "Epoch: 450/20000, Loss: 0.11271971\n",
      "Epoch: 460/20000, Loss: 0.10994914\n",
      "Epoch: 470/20000, Loss: 0.10728056\n",
      "Epoch: 480/20000, Loss: 0.10471058\n",
      "Epoch: 490/20000, Loss: 0.10223591\n",
      "Epoch: 500/20000, Loss: 0.09985338\n",
      "Epoch: 510/20000, Loss: 0.09755988\n",
      "Epoch: 520/20000, Loss: 0.09535244\n",
      "Epoch: 530/20000, Loss: 0.09322812\n",
      "Epoch: 540/20000, Loss: 0.09118416\n",
      "Epoch: 550/20000, Loss: 0.08921776\n",
      "Epoch: 560/20000, Loss: 0.08732627\n",
      "Epoch: 570/20000, Loss: 0.08550702\n",
      "Epoch: 580/20000, Loss: 0.08375744\n",
      "Epoch: 590/20000, Loss: 0.08207483\n",
      "Epoch: 600/20000, Loss: 0.08045626\n",
      "Epoch: 610/20000, Loss: 0.07889789\n",
      "Epoch: 620/20000, Loss: 0.07739072\n",
      "Epoch: 630/20000, Loss: 0.07589137\n",
      "Epoch: 640/20000, Loss: 0.07435710\n",
      "Epoch: 650/20000, Loss: 0.07275510\n",
      "Epoch: 660/20000, Loss: 0.07107297\n",
      "Epoch: 670/20000, Loss: 0.06942891\n",
      "Epoch: 680/20000, Loss: 0.06780214\n",
      "Epoch: 690/20000, Loss: 0.06621229\n",
      "Epoch: 700/20000, Loss: 0.06467836\n",
      "Epoch: 710/20000, Loss: 0.06318659\n",
      "Epoch: 720/20000, Loss: 0.06174183\n",
      "Epoch: 730/20000, Loss: 0.06034444\n",
      "Epoch: 740/20000, Loss: 0.05898939\n",
      "Epoch: 750/20000, Loss: 0.05767188\n",
      "Epoch: 760/20000, Loss: 0.05638803\n",
      "Epoch: 770/20000, Loss: 0.05513497\n",
      "Epoch: 780/20000, Loss: 0.05391100\n",
      "Epoch: 790/20000, Loss: 0.05271528\n",
      "Epoch: 800/20000, Loss: 0.05154702\n",
      "Epoch: 810/20000, Loss: 0.05040523\n",
      "Epoch: 820/20000, Loss: 0.04928898\n",
      "Epoch: 830/20000, Loss: 0.04819742\n",
      "Epoch: 840/20000, Loss: 0.04712987\n",
      "Epoch: 850/20000, Loss: 0.04608574\n",
      "Epoch: 860/20000, Loss: 0.04506447\n",
      "Epoch: 870/20000, Loss: 0.04406552\n",
      "Epoch: 880/20000, Loss: 0.04308833\n",
      "Epoch: 890/20000, Loss: 0.04213238\n",
      "Epoch: 900/20000, Loss: 0.04119715\n",
      "Epoch: 910/20000, Loss: 0.04028219\n",
      "Epoch: 920/20000, Loss: 0.03938703\n",
      "Epoch: 930/20000, Loss: 0.03851130\n",
      "Epoch: 940/20000, Loss: 0.03765463\n",
      "Epoch: 950/20000, Loss: 0.03681667\n",
      "Epoch: 960/20000, Loss: 0.03599713\n",
      "Epoch: 970/20000, Loss: 0.03519573\n",
      "Epoch: 980/20000, Loss: 0.03441216\n",
      "Epoch: 990/20000, Loss: 0.03364615\n",
      "Epoch: 1000/20000, Loss: 0.03289741\n",
      "Epoch: 1010/20000, Loss: 0.03216564\n",
      "Epoch: 1020/20000, Loss: 0.03145052\n",
      "Epoch: 1030/20000, Loss: 0.03075171\n",
      "Epoch: 1040/20000, Loss: 0.03006889\n",
      "Epoch: 1050/20000, Loss: 0.02940168\n",
      "Epoch: 1060/20000, Loss: 0.02874976\n",
      "Epoch: 1070/20000, Loss: 0.02811278\n",
      "Epoch: 1080/20000, Loss: 0.02749044\n",
      "Epoch: 1090/20000, Loss: 0.02688243\n",
      "Epoch: 1100/20000, Loss: 0.02628845\n",
      "Epoch: 1110/20000, Loss: 0.02570823\n",
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      "Epoch: 1170/20000, Loss: 0.02250005\n",
      "Epoch: 1180/20000, Loss: 0.02200832\n",
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      "Epoch: 1290/20000, Loss: 0.01731290\n",
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      "Epoch: 1500/20000, Loss: 0.01121260\n",
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      "Epoch: 1800/20000, Loss: 0.00646751\n",
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     ]
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
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     ]
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
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      "Epoch: 19960/20000, Loss: 0.00000001\n",
      "Epoch: 19970/20000, Loss: 0.00000001\n",
      "Epoch: 19980/20000, Loss: 0.00000001\n",
      "Epoch: 19990/20000, Loss: 0.00000001\n",
      "Epoch: 20000/20000, Loss: 0.00000001\n"
     ]
    }
   ],
   "source": [
    "# Create coRNN instance\n",
    "cornn = coRNN(input_size, hidden_size, output_size, dt=0.1, gamma=1.0, epsilon=0.01)\n",
    "\n",
    "# Loss and optimizer\n",
    "criterion = nn.MSELoss()\n",
    "optimizer = torch.optim.Adam(cornn.parameters(), lr=0.001)\n",
    "\n",
    "# Training loop\n",
    "for epoch in range(num_epochs):\n",
    "    # Forward pass\n",
    "    output = cornn(input_tensor)\n",
    "    loss = criterion(output, target_tensor)\n",
    "\n",
    "    # Backward and optimize\n",
    "    optimizer.zero_grad()\n",
    "    loss.backward()\n",
    "    optimizer.step()\n",
    "\n",
    "    # Print progress\n",
    "    if (epoch+1) % 10 == 0:\n",
    "        print(f'Epoch: {epoch+1}/{num_epochs}, Loss: {loss.item():.8f}')\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "767aba97",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([1, 1, 201])\n",
      "torch.Size([1, 20, 201])\n"
     ]
    }
   ],
   "source": [
    "print(test_tensor.shape)\n",
    "prediction_tensor = torch.zeros(1, 20, 201).float()\n",
    "print(prediction_tensor.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "f3b34404",
   "metadata": {},
   "outputs": [],
   "source": [
    "with torch.no_grad():\n",
    "    prediction = cornn(test_tensor)\n",
    "    prediction = prediction.view(1, 1, 201).float()\n",
    "    prediction_tensor[:, 0, :] = prediction\n",
    "    for i in range(19):\n",
    "        prediction = cornn(prediction)\n",
    "        prediction = prediction.view(1, 1, 201).float()\n",
    "        prediction_tensor[:, i+1, :] = prediction"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1e8a48dd",
   "metadata": {},
   "source": [
    "### errors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "44016d8f",
   "metadata": {},
   "outputs": [],
   "source": [
    "### L2 norm error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "a17a3441",
   "metadata": {},
   "outputs": [],
   "source": [
    "# # exact\n",
    "# u_test = u\n",
    "# u_test_full = u_test[80:100, :]\n",
    "# prediction_tensor = torch.squeeze(prediction_tensor)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "23f878f0",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "# k1 = (prediction_tensor - u_test_full)**2\n",
    "# u_test_full_tensor = torch.tensor(u_test_full**2)\n",
    "# prediction_tensor.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "4b754a14",
   "metadata": {},
   "outputs": [],
   "source": [
    "# # Compute the relative L2 error norm (generalization error)\n",
    "# relative_error_test = torch.mean(k1)/ torch.mean(u_test_full_tensor)\n",
    "\n",
    "# print(\"Relative Error Test: \", relative_error_test.item(), \"%\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e2bddd71",
   "metadata": {},
   "source": [
    "### max absolute error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "82622bae",
   "metadata": {},
   "outputs": [],
   "source": [
    "# # R_abs = torch.max(prediction_tensor-u_test_full)\n",
    "# print(R_abs)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f5edaee1",
   "metadata": {},
   "source": [
    "### Explained variance score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "420daaea",
   "metadata": {},
   "outputs": [],
   "source": [
    "# import torch\n",
    "\n",
    "# a = prediction_tensor\n",
    "# b = u_test_full\n",
    "# # Assuming 'a' is your predicted values (model's predictions) and 'b' is the true values (ground truth)\n",
    "# # Make sure 'a' and 'b' are PyTorch tensors\n",
    "# b = torch.tensor(b)\n",
    "# # Calculate the mean of 'b'\n",
    "# mean_b = torch.mean(b)\n",
    "\n",
    "# # Calculate the Explained Variance Score\n",
    "# numerator = torch.var(b - a)  # Variance of the differences between 'b' and 'a'\n",
    "# denominator = torch.var(b)    # Variance of 'b'\n",
    "# evs = 1 - numerator / denominator\n",
    "\n",
    "# print(\"Explained Variance Score:\", evs.item())\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1fcf5684",
   "metadata": {},
   "source": [
    "### mean absolute error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "1cc57baa",
   "metadata": {},
   "outputs": [],
   "source": [
    "# R_mean = torch.mean(torch.abs(prediction_tensor - u_test_full))\n",
    "# print(R_mean)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "90905607",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(101, 201)\n"
     ]
    }
   ],
   "source": [
    "print(u.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "3c88215b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Exact Solution\n",
    "\n",
    "u_test = u\n",
    "u_test_full = u_test[80:100, :]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "4a264091",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([1, 1, 201])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prediction.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "ad9cc704",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(20, 201)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u_test_full.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2d6ddd1f",
   "metadata": {},
   "source": [
    "### L2 norm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "f2ea8557",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([20, 201])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Extrapolation\n",
    "\n",
    "k1 = ( prediction_tensor - u_test_full)**2\n",
    "u_test_full_tensor = torch.tensor(u_test_full**2)\n",
    "u_test_full_tensor.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "96b1b0bf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Relative Error Test:  0.005146909499120122 %\n"
     ]
    }
   ],
   "source": [
    "# Compute the relative L2 error norm (generalization error)\n",
    "relative_error_test = torch.mean(k1)/ torch.mean(u_test_full_tensor)\n",
    "\n",
    "print(\"Relative Error Test: \", relative_error_test.item(), \"%\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "54bab42a",
   "metadata": {},
   "source": [
    "### Max absolute error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "914e145e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor(0.3201, dtype=torch.float64)\n"
     ]
    }
   ],
   "source": [
    "R_abs = torch.max(torch.abs(prediction_tensor - u_test_full))\n",
    "print(R_abs)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "48e97ee7",
   "metadata": {},
   "source": [
    "### Explained variance score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "308706cf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Explained Variance Score: 0.9954673939400089\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_36381/2104891356.py:7: UserWarning: To copy construct from a tensor, it is recommended to use sourceTensor.clone().detach() or sourceTensor.clone().detach().requires_grad_(True), rather than torch.tensor(sourceTensor).\n",
      "  a = torch.tensor(a)\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "\n",
    "a = prediction_tensor\n",
    "b = u_test_full\n",
    "# Assuming 'a' is your predicted values (model's predictions) and 'b' is the true values (ground truth)\n",
    "# Make sure 'a' and 'b' are PyTorch tensors\n",
    "a = torch.tensor(a)\n",
    "b = torch.tensor(b)\n",
    "# Calculate the mean of 'b'\n",
    "mean_b = torch.mean(b)\n",
    "\n",
    "# Calculate the Explained Variance Score\n",
    "numerator = torch.var(b - a)  # Variance of the differences between 'b' and 'a'\n",
    "denominator = torch.var(b)    # Variance of 'b'\n",
    "evs = 1 - numerator / denominator\n",
    "\n",
    "print(\"Explained Variance Score:\", evs.item())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb1a3ac9",
   "metadata": {},
   "source": [
    "### Mean absolute error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "fe1dc182",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Relative Error Test:  tensor(0.0356, dtype=torch.float64) %\n"
     ]
    }
   ],
   "source": [
    "# Compute the relative L2 error norm (generalization error)\n",
    "relative_error_test = torch.mean(torch.abs(prediction_tensor - u_test_full))\n",
    "\n",
    "print(\"Relative Error Test: \", relative_error_test, \"%\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5547b4aa",
   "metadata": {},
   "source": [
    "### snapshots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "26e04752",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([20, 201])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prediction_tensor = torch.squeeze(prediction_tensor)\n",
    "prediction_tensor.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "450f182b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import torch\n",
    "\n",
    "# Create the figure and axis objects with reduced width\n",
    "fig, ax = plt.subplots(figsize=(5, 5))  # You can adjust the width (7 inches) and height (5 inches) as needed\n",
    "\n",
    "# # Make sure the font is Times Roman\n",
    "# plt.rcParams['font.family'] = 'Times New Roman'\n",
    "\n",
    "# # Perform the prediction\n",
    "# with torch.no_grad():\n",
    "#     prediction = lem(test_tensor)\n",
    "\n",
    "final_time_output = prediction_tensor[-2, :]\n",
    "final_out = final_time_output.detach().numpy().reshape(-1, 1)\n",
    "final_true = u[-2, :].reshape(-1, 1)\n",
    "\n",
    "# Plot the data with red and blue lines, one with dotted and one with solid style\n",
    "ax.plot(x.T, final_out, color='red', linestyle='dotted', linewidth=12, label='Prediction')\n",
    "ax.plot(x.T, final_true, color='blue', linestyle='solid', linewidth=7, label='True')\n",
    "\n",
    "# Set the axis labels with bold font weight\n",
    "ax.set_xlabel(r\"${x}$\", fontsize=26, color='black', fontdict={'weight': 'bold'})\n",
    "ax.set_ylabel(r\"${u(x, t)}$\", fontsize=26, color='black', fontdict={'weight': 'bold'})\n",
    "\n",
    "# Set the title with bold font weight\n",
    "ax.set_title(r\"${t = 0.99}$\", fontsize=26, color='black', fontweight='bold')\n",
    "\n",
    "# Set the number of ticks for x-axis and y-axis to 3\n",
    "ax.set_xticks([-1, 0, 1])\n",
    "ax.set_yticks([-1, 0, 1])\n",
    "\n",
    "# Set tick labels fontweight to bold and increase font size\n",
    "ax.tick_params(axis='both', which='major', labelsize=20, width=2, length=10)\n",
    "\n",
    "# # Set the fontweight for tick labels to bold\n",
    "# for tick in ax.get_xticklabels() + ax.get_yticklabels():\n",
    "#     tick.set_weight('bold')\n",
    "\n",
    "# Set the spines linewidth to bold\n",
    "ax.spines['top'].set_linewidth(2)\n",
    "ax.spines['right'].set_linewidth(2)\n",
    "ax.spines['bottom'].set_linewidth(2)\n",
    "ax.spines['left'].set_linewidth(2)\n",
    "\n",
    "\n",
    "# Increase font size for x and y axis numbers\n",
    "ax.tick_params(axis='both', which='major', labelsize=24)\n",
    "\n",
    "# Set the legend\n",
    "# ax.legend()\n",
    "\n",
    "plt.savefig('coRNN_0.99_20.pdf', dpi=500, bbox_inches=\"tight\")\n",
    "\n",
    "# Show the plot\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "fcf131ac",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import torch\n",
    "\n",
    "# Create the figure and axis objects with reduced width\n",
    "fig, ax = plt.subplots(figsize=(5, 5))  # You can adjust the width (7 inches) and height (5 inches) as needed\n",
    "\n",
    "\n",
    "\n",
    "final_time_output = prediction_tensor[-20, :]\n",
    "final_out = final_time_output.detach().numpy().reshape(-1, 1)\n",
    "final_true = u[-20, :].reshape(-1, 1)\n",
    "\n",
    "# Plot the data with red and blue lines, one with dotted and one with solid style\n",
    "ax.plot(x.T, final_out, color='red', linestyle='dotted', linewidth=12, label='Prediction')\n",
    "ax.plot(x.T, final_true, color='blue', linestyle='solid', linewidth=7, label='True')\n",
    "\n",
    "# Set the axis labels with bold font weight\n",
    "ax.set_xlabel(r\"${x}$\", fontsize=26, color='black', fontdict={'weight': 'bold'})\n",
    "ax.set_ylabel(r\"${u(x, t)}$\", fontsize=26, color='black', fontdict={'weight': 'bold'})\n",
    "\n",
    "# Set the title with bold font weight\n",
    "ax.set_title(r\"${t = 0.81}$\", fontsize=26, color='black', fontweight='bold')\n",
    "\n",
    "# Set the number of ticks for x-axis and y-axis to 3\n",
    "ax.set_xticks([-1, 0, 1])\n",
    "ax.set_yticks([-1, 0, 1])\n",
    "\n",
    "# Set tick labels fontweight to bold and increase font size\n",
    "ax.tick_params(axis='both', which='major', labelsize=20, width=2, length=10)\n",
    "\n",
    "# # Set the fontweight for tick labels to bold\n",
    "# for tick in ax.get_xticklabels() + ax.get_yticklabels():\n",
    "#     tick.set_weight('bold')\n",
    "\n",
    "# Set the spines linewidth to bold\n",
    "ax.spines['top'].set_linewidth(2)\n",
    "ax.spines['right'].set_linewidth(2)\n",
    "ax.spines['bottom'].set_linewidth(2)\n",
    "ax.spines['left'].set_linewidth(2)\n",
    "\n",
    "# Set the legend\n",
    "# ax.legend()\n",
    "\n",
    "plt.savefig('coRNN_0.81_20.pdf', dpi=500, bbox_inches=\"tight\")\n",
    "\n",
    "# Show the plot\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "25bccfef",
   "metadata": {},
   "source": [
    "### 80-20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "c0ba851a",
   "metadata": {},
   "outputs": [],
   "source": [
    "conc_u = torch.squeeze(input_tensor)\n",
    "prediction_tensor = torch.squeeze(prediction_tensor)\n",
    "concatenated_tensor = torch.cat((conc_u, prediction_tensor), dim=0)\n",
    "t1 = np.linspace(0, 1 , 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "e42582e8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import torch\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.ticker import FixedLocator\n",
    "\n",
    "# Assuming you have defined concatenated_tensor as a PyTorch tensor\n",
    "# concatenated_tensor = torch.cat((tensor1, tensor2), dim=0)\n",
    "\n",
    "# Convert concatenated_tensor to a NumPy array\n",
    "concatenated_array = concatenated_tensor.numpy()\n",
    "\n",
    "# Define custom color levels\n",
    "x = np.linspace(-1, 1, concatenated_array.shape[1])  # Replace 0 and 1 with your actual x range\n",
    "t = np.linspace(0, 1, concatenated_array.shape[0])  # Replace 0 and 1 with your actual t range\n",
    "X, T = np.meshgrid(x, t1)\n",
    "\n",
    "# Define custom color levels using the minimum and maximum from the NumPy array\n",
    "c_levels = np.linspace(np.min(concatenated_array), np.max(concatenated_array), 400)\n",
    "\n",
    "# Plot the contour with interpolated data\n",
    "plt.figure(figsize=(20, 5))\n",
    "plt.pcolormesh(T, X, concatenated_array, shading='auto', cmap='coolwarm')\n",
    "\n",
    "# Set the fontweight for axis labels to regular (not bold)\n",
    "plt.xlabel(\"$t$\", fontsize=26)\n",
    "plt.ylabel(\"$x$\", fontsize=26)\n",
    "plt.title(\"$u(x, t)$\", fontsize=26)\n",
    "\n",
    "# Set tick labels fontweight to regular (not bold) and increase font size\n",
    "plt.tick_params(axis='both', which='major', labelsize=20, width=3, length=10)\n",
    "\n",
    "# Set the fontweight for tick labels to regular (not bold)\n",
    "for tick in plt.gca().get_xticklabels() + plt.gca().get_yticklabels():\n",
    "    tick.set_weight('normal')\n",
    "\n",
    "# Set the number of ticks for x-axis and y-axis to 5\n",
    "num_ticks = 5\n",
    "x_ticks = np.linspace(np.min(T), np.max(T), num_ticks)\n",
    "y_ticks = np.linspace(np.min(X), np.max(X), num_ticks)\n",
    "\n",
    "plt.gca().xaxis.set_major_locator(FixedLocator(x_ticks))\n",
    "plt.gca().yaxis.set_major_locator(FixedLocator(y_ticks))\n",
    "\n",
    "cbar1 = plt.colorbar()\n",
    "# Set the number of ticks for the color bar with uniformly distributed numbers\n",
    "num_ticks = 5\n",
    "c_ticks = np.linspace(np.min(concatenated_array), np.max(concatenated_array), num_ticks)\n",
    "cbar1.set_ticks(c_ticks)\n",
    "\n",
    "# Set the fontweight and fontsize for color bar tick labels\n",
    "for t in cbar1.ax.get_yticklabels():\n",
    "    t.set_weight('normal')\n",
    "    t.set_fontsize(26)  # Increase the font size for color bar tick labels\n",
    "\n",
    "# Increase the size of numbers on axis and color bar\n",
    "plt.xticks(fontsize=26)\n",
    "plt.yticks(fontsize=26)\n",
    "\n",
    "# Increase the tick size and width of the color bar\n",
    "cbar1.ax.tick_params(axis='both', which='major', labelsize=30, width=3,  length=10)\n",
    "\n",
    "# Add a dotted line at t = 0.8\n",
    "plt.axvline(x=0.8, color='black', linestyle='dotted', linewidth=5)\n",
    "\n",
    "#plt.savefig('Contour_LEM_20.pdf', dpi=500, bbox_inches=\"tight\")\n",
    "plt.savefig('contour_coRNN_20.jpeg', dpi=500, bbox_inches=\"tight\")\n",
    "# Show the plot\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1e47d879",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "pytorch",
   "language": "python",
   "name": "pytorch"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
